Nonextensive statistical field theory

We introduce a field-theoretic approach for describing the critical behavior of nonextensive systems, systems displaying global correlations among their degrees of freedom, encoded by the nonextensive parameter $q$. As some applications, we report, to our knowledge, the first analytical computation of both universal static and dynamic $q$-dependent nonextensive critical exponents for O($N$) vector models, valid for all loop orders and $|q - 1| < 1$. Then emerges the new nonextensive O($N$)$_{q}$ universality class. We employ six independent methods which furnish identical results. Particularly, the results for nonextensive 2d Ising systems, exact within the referred approximation, agree with that obtained from computer simulations, within the margin of error, as better as $q$ is closer to $1$. We argue that the present approach can be applied to all models described by extensive statistical field theory as well. The results show an interplay between global correlations and fluctuations.